Download Final 1 Practice

AP PHYSICS FINAL 1 PRACTICE TEST
NAME_________________________________
MULTIPLE CHOICE – Put your answers to the multiple choice questions here:
Question
Your
Answer
Question
Your
Answer
1
2
3
4
5
6
7
8
D
C
E
A
E
D
B
A
9
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A
A
C
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A
1. The position of an object is given as a function of time by 𝑥 = 7𝑡 − 3𝑡 2 , where x is in meters,
and t is in seconds. Its average velocity over the interval from 𝑡 = 2 to 𝑡 = 4 is
A. 5 m/s
B –5 m/s
C. 11 m/s
D. –11 m/s
E. –14.5 m/s
2. An object is thrown vertically into the air. Which of the following five graphs represents
the velocity of the object as a function of time? Upward is positive.
3. Two objects are traveling around different circular orbits with constant speed. They both
have the same acceleration but object A is traveling twice as fast as object B. The orbit
radius for object A is _____ the orbit radius for object B.
A. one-fourth B. one-half
C. the same as
D. twice
E. four times
4. A girl wishes to swim across a river to a point
directly opposite, as shown at right. She can swim
at 2 m/s in still water and the river is flowing at 1
m/s. At what angle 𝜃 with respect to the line
joining the starting and finishing points should she
swim?
A. 30º
B. 45º
C. 60º
D. 63º
E. 90º
5. A crate rests on a
horizontal surface
and a person pulls
on it with a 10-N
force. Rank the
situations shown at
right according to the magnitude of the normal force exerted by the surface on the
crate, least to greatest.
A. 1,2,3
B. 2,1,3
C. 2,3,1
D. 1,3,2
E. 3,2,1
6. A mass m moves on a curved path from point 𝑋 to point 𝑌. Which of the diagrams at right
indicates a possible combination of the net force 𝐹 on the mass, and the velocity 𝑣 and
acceleration 𝑎 of the mass at the location shown?
7. The position of an object is given as a function of time by 𝑥 = 16𝑡 − 3𝑡 3 , where x is in
meters, and t is in seconds. The particle is momentarily at rest as 𝑡 =
A. 0.75 s
B. 1.3 s
C. 5.3 s
D. 7.3 s
E. 9.3 s
8. A block of mass 𝑚 is pulled at constant velocity along
⃗ as
a rough horizontal floor by an applied force 𝑇
shown. The magnitude of the frictional force is
A. 𝑇𝑐𝑜𝑠𝜃
B. 𝑇𝑠𝑖𝑛𝜃
C. zero
D. 𝑚𝑔
E. 𝑚𝑔𝑐𝑜𝑠𝜃
9. A stone is thrown horizontally and follows the path XYZ
shown at right. The direction of the acceleration of the
stone at point Y is
A.
B.
C.
D.
E.
10. Block 𝐴, with a mass of 50 kg, rests on a horizontal table top.
The coefficient of static friction is 0.40. A horizontal string is
attached to 𝐴, passes over a massless, frictionless pulley, and
then is attached to block 𝐵, which hangs freely. The smallest
mass 𝑚𝐵 of block 𝐵 that will start block 𝐴 moving is
A. 20 kg
B. 30 kg
C. 40 kg
D. 50 kg
E. 70 kg
11. A ball is held at a height 𝐻 above a floor. It is then released and falls to the floor. If air
resistance can be ignored, which of the five graphs below correctly gives the
gravitational potential energy of the ball as a function of the altitude 𝑦 of the ball?
U
U
U
U
U
12. A particle is released from rest at the point 𝑥 =
𝑎 and moves along the 𝑥 axis subject to the
potential energy function shown at right. The
particle
A. moves to a point to the left of 𝑥 = 𝑒, stops,
and remains at rest
B. moves to the point 𝑥 = 𝑒, then moves to the
left
C. moves to infinity at varying speeds
D. moves to 𝑥 = 𝑏, where it remains at rest
E. moves to 𝑥 = 𝑒 and then to 𝑥 = 𝑑, where it
remains at rest
13. When a certain rubber band is stretched a distance 𝑥, it exerts a restoring force of
magnitude 𝐹 = 𝑎𝑥 + 𝑏𝑥 2 , where a and b are constants. The work done in stretching this
rubber band from 𝑥 = 0 to 𝑥 = 𝐿 is
1
1
A. 𝑎𝐿2 + 𝑏𝐿𝑥 3 B. 𝑎𝐿 + 2𝑏𝐿2
C. 𝑎 + 2𝑏𝐿
D. 𝑏𝐿
E. 2 𝑎𝐿2 + 3 𝑏𝐿3
14. An elevator is rising at constant speed. Consider the following statements:
I. the upward cable force is constant
II. the kinetic energy of the elevator is constant
III. the gravitational potential energy of the elevator is constant
IV. the acceleration of the elevator is zero
V. the mechanical energy of the elevator is constant
A. all five are true
D. only I, II, and III are true
B. only II and V are true
E. only I, II, and IV are true
C. only IV and V are true
15. A particle has a displacement 𝑟 = (5𝑖̂ − 3𝑘̂) 𝑚 while being acted upon by a constant
force 𝐹 = (4𝑖̂ + 2𝑗̂ − 4𝑘̂) 𝑁. The work done on the particle by this force is
A. 20 J
B. 32 J
C. 12 J
D. 10 J
E. 14 J
16. A block of mass 𝑚 is initially moving to the right on a horizontal frictionless surface at a
speed 𝑣. It then compresses a spring of spring constant 𝑘. At the instant when the kinetic
energy of the block is equal to the potential energy of the spring, the spring is
compressed a distance of
𝑚
A. 𝑣√2𝑘
1
B. 2 𝑚𝑣 2
1
C. 4 𝑚𝑣 2
D.
𝑚𝑣 2
4𝑘
1
𝑚𝑣
E. 4 √
𝑘
FREE RESPONSE PROBLEMS – Show your work for partial credit. Circle or box your answers.
Include the correct units and the correct number of significant figures in your answers!
1. A 0.10-kilogram solid rubber ball is
attached to the end of a 0.80-meter
length of light thread. The ball is swung in
a vertical circle, as shown in the diagram.
Point P, the lowest point of the circle, is
0.20 meter above the floor. The speed of
the ball at the top of the circle is 6.0
meters per second, and the total energy
of the ball is kept constant.
(a) Determine the speed of the ball at
point P, the lowest point of the circle.
(b) Determine the tension in the thread at the top of the circle.
(c) Determine the tension in the thread at the bottom of the circle.
‘
(d) The thread breaks when the ball is at the lowest point of the circle. Determine the
horizontal distance that the ball travels (from point P) before hitting the floor.
(e) You measure the speed of the ball at the lowest point of the circle, and find that it is
only 7.8 m/s. Determine the work done by air friction on the ball as it swung down from
the highest point to the lowest point.
2. A skier of mass m will be pulled up a hill by a rope, as
shown at right. The magnitude of the acceleration of
the skier as a function of time t can be modeled by the
equations
where 𝑎𝑚𝑎𝑥 and T are constants. The hill is inclined at
an angle  above the horizontal, and friction between the skis and the snow is negligible.
Express your answers in terms of given quantities and fundamental constants.
(a) Derive an expression for the velocity of the skier as a function of time during the
acceleration. Assume the skier starts from rest.
(b) Derive an expression for the work done by the net force on the skier from rest until
terminal speed is reached.
(c) Determine the magnitude of the force exerted by the rope on the skier at terminal speed.
(d) Suppose that the magnitude of the acceleration is instead modeled as
for all t > 0 , where amax and T are the same as in the original model. On the axes below,
sketch the graphs of the force exerted by the rope on the skier for the two models, from t = 0
to a time t > T . Label the original model and the new model.
3. An amusement park ride
features a passenger
compartment of mass M that is
released from rest at point A, as
shown in the figure above, and
moves along a track to point E.
The compartment is in free fall
between points A and B, which
3𝑅
are a distance of 4 apart, then
moves along the circular arc of
radius R between points B and D.
Assume the track is frictionless
from point A to point D and the dimensions of the passenger compartment are negligible
compared to R.
(a) On the dot below that represents the passenger compartment, draw and label the
forces (not components) that act on the passenger compartment when it is at point C,
which is at an angle 𝜃 from point B.
(b) In terms of 𝜃 and the magnitudes of the forces drawn in part (a), determine an
expression for the magnitude of the centripetal force acting on the compartment at
point C. If you need to draw anything besides what you have shown in part (a) to assist in
your solution, use the space below. Do NOT add anything to the figure in part (a).
(c) Derive an expression for the speed 𝑣𝐷 of the passenger compartment as it reaches
point D in terms of M, R, and fundamental constants, as appropriate.
A force acts on the compartment between points D and E and brings it to rest at point E.
(d) Suppose the compartment is brought to rest by friction. Calculate the numerical
value of the coefficient of friction 𝜇 between the compartment and the track.
(e) Now consider the case in which there is no friction between the compartment and
the track, but instead the compartment is brought to rest by a braking force −𝑘𝒗, where k
is a constant and 𝒗 is the velocity of the compartment. Express all algebraic answers to
the following in terms of M, R, k, 𝑣, and fundamental constants, as appropriate.
i. Derive an expression for the acceleration 𝑎 of the compartment.
ii. On the axes below, sketch a graph of the magnitude of the acceleration of the
compartment as a function of time. On the axes, explicitly label any intercepts,
asymptotes, maxima, or minima with numerical values of algebraic expressions, as
appropriate.